I have a question about the general rules for using certain weight yarns with needles...
I have a needle size gauge that also gives the appropriate weight yarn to use with that size needles. My question is, what if you have bigger or smaller needles? For example, I have a light weight yarn, that indicates using a size 5 or 6 needle, but a pattern that calls for size 8 needles. Can I use light weight yarn with larger needles, and if so, what is the effect on the stitch. What about if I did vice-versa - bulkier weight yarn with smaller needles.

Any guidance would be great...just curious as to if I HAVE to stick to what a pattern says as far as weight of yarn and needles, or if I can change it up, and if I can how the best way to do it is...

The stitches will be looser and more open than if you knit the yarn on the smaller needles. I prefer knitting with a larger needle even going up to a 9 or 10 for a yarn that's supposed to be knit on as 5 or 6. You may like it or you may not; if you're just practicing knitting or making a scarf, it doesn't matter so much. But if you're following a pattern that needs to fit - a sweater, a hat, mittens - you would have to adjust the sts used or do another size of the pattern to make it fit correctly.

Same thing with using a heavier yarn on smaller needles; it will be really tight and densely knit and you may not like the effect.

I meant that they will be looser and more open if you use larger needles than if you knit them on smaller needles. I thought that was her question but I see that she said 'use larger or smaller needles'.

Thanks ladies! What I'm trying to do is knit a baby hat. I have yarn that is lightweight (3) but the DPNs I have are 9s...I want it to be for a newborn, so I think that I should stick with using the smaller size needles; I don't want a loose stitch.
Now, The pattern calls for size 8 needles, but the yarn is calling for size 6, and like I said, I want to use smaller needles...
Based on your posts, you're saying (let me know if this is right) that I will have to adjust the number of stitches that I use to make the hat the right size because I will be using smaller needles; I assume that I will need more stitches then...so I may have to cast on more than the pattern calls for to make up for the fact that the stitches will be smaller...
Did I get it right?? LOL!

Yes, that's the right conclusion to come to. Sometimes though, the lighter weight yarn can be knit with the same stitch number on a larger needle and it will com out okay. So go ahead and try the yarn on size 9s and see if the knit fabric is going to be too thin before you buy other needles.

When it comes to things like this I always imagine knitting sewing thread on size 15s, and that generally answers that question. It's when you're in a one off situation where you have to seriously consider if it's going to make a difference.

I have one hat pattern that calls for two strands of worsted or one strand of super bulky. I've done it both ways and really liked the results.

When there is a question as to this kind of thing, knit a swatch. I have billions of them to test gauge on new yarns and needles.

I lately found a jacket pattern online (where?!? knitty.com?!?) with a cable-stripe design. And the thing was nicely fitted around the waist: by going to smaller needles and just following the pattern. this was a great showing of the effect of smaller needles and also a neat trick if you don't have room in your pattern to decrease or increase...

I would not go endlessly far with bigger or smaller / larger needles... really thin on large needles will be no real fabric anymore - and not usable lace.
really thick on small needles will be a pain to knit. stuffy and cramped...

but within the middle range you can always change....

If you have a coil of yarn to play around with: knit swatches with 4 or 5 different sizes (and attach little notes about the needle size). when you compare those swatches now, you will be surprised.

Do not stick to patterns toooooo closely anyways. Start to read and to feel your pattern and try to find out, how and where you want to differ from the pattern anyways (fit, shape, length, pattern, etc...)